Jian-Ci Xiao
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·Research Field
My interests focus mainly on fractal geometry and related topics, especially:
Topological properties of fractal sets, e.g., homeomorphism criteria between generalized Sierpinski carpets, behaviour of connected components of self-similar sets.
Geometric properties of fractal sets, e.g., self-embedding maps of self-similar and self-affine sets, interior of self-similar sets and their sumsets or difference sets, Falconer’s distance conjecture.
Dimension theory of fractal sets, e.g., fractal dimensions (box, Hausdorff, topological Hausdorff, etc.) of fractal sets and their relationship.